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1. Let X1, ..., Xn are iid Bernoulli(0) random variables. (a) Find a level a large sample likelihood ratio test for testing Ho : 0 = 00 versus Ha : 0 > 00. (b) Find a level a large sample likelihood ratio test for testing Ho : 0 = 00 versus Ha : 0 # 00. (c) Suppose that in a survey of 90 people from the university campus, 68 people supported legalizing abortion. Let 0 be the probability that a randomly chosen subject from the university campus supports legalizing abortion. Apply the above results of a) to test i) Ho : 0 = 0.6 versus Ha : 0 > 0.6 at the 5% level, ii) by inverting the test construct a 95% CI for 0, iii) calculate the power of the test when 0 = 0.65, iv) calculate the power of the test when 0 = 0.7, v) what would be the required sample size if we want 90% power when 0 = 0.7. (d) Suppose that in a survey of 80 people from the university campus, 35 favor the university not receiving corporate funding. Let 0 be the probability that a randomly chosen subject from the university campus supports the university not receiving any corporate funding. Apply the above results of b) to test i) Ho : 0 = 0.5 versus Ha : 0 # 0.5 at the 5% level, ii) by inverting the test construct a 95% CI for 0, iii) calculate the power of the test when 0 = 0.45, iv) what is the power of the test when 0 = 0.5, v) what would be the required sample size if we want 90% power when 0 = 0.55